Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGS

TL;DR

This paper introduces a global Gaussian reduction method for 3D Gaussian Splatting using optimal transport, significantly reducing primitives while maintaining rendering quality and outperforming existing techniques.

Contribution

It presents a novel optimal transport-based approach for global Gaussian mixture reduction in 3DGS, improving efficiency and fidelity over prior heuristics.

Findings

Achieves negligible quality loss with only 10% Gaussians.

Outperforms state-of-the-art compaction methods.

Applicable to various stages of 3DGS pipelines.

Abstract

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for radiance field rendering, but it typically requires millions of redundant Gaussian primitives, overwhelming memory and rendering budgets. Existing compaction approaches address this by pruning Gaussians based on heuristic importance scores, without global fidelity guarantee. To bridge this gap, we propose a novel optimal transport perspective that casts 3DGS compaction as global Gaussian mixture reduction. Specifically, we first minimize the composite transport divergence over a KD-tree partition to produce a compact geometric representation, and then decouple appearance from geometry by fine-tuning color and opacity attributes with far fewer Gaussian primitives. Experiments on benchmark datasets show that our method (i) yields negligible loss in rendering quality (PSNR, SSIM, LPIPS) compared to vanilla 3DGS with only 10% Gaussians; and (ii) consistently outperforms state-of-the-art 3DGS compaction techniques. Notably, our method is applicable to any stage of vanilla or accelerated 3DGS pipelines, providing an efficient and agnostic pathway to lightweight neural rendering. The code is publicly available at https://github.com/DrunkenPoet/GHAP